Solve 4/t-4-1/2t/t+2=0

$$\frac { 4 } { t } - \frac { 4 - \frac { 1 } { 2 } t } { t + 2 } = 0$$

Solve for t

$$t=-4i$$

$$t=4i$$

Steps by Finding Square Root

Variable t cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by t\left(t+2\right), the least common multiple of t,t+2.

$$\left(t+2\right)\times 4-t\left(4-\frac{1}{2}t\right)=0$$

Use the distributive property to multiply t+2 by 4.

$$4t+8-t\left(4-\frac{1}{2}t\right)=0$$

Use the distributive property to multiply t by 4-\frac{1}{2}t.

$$4t+8-\left(4t-\frac{1}{2}t^{2}\right)=0$$

To find the opposite of 4t-\frac{1}{2}t^{2}, find the opposite of each term.

$$4t+8-4t+\frac{1}{2}t^{2}=0$$

Combine 4t and -4t to get 0.

$$8+\frac{1}{2}t^{2}=0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$\frac{1}{2}t^{2}=-8$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$t^{2}=-8\times 2$$

Multiply -8 and 2 to get -16.

$$t^{2}=-16$$

The equation is now solved.

$$t=4i t=-4i$$

Steps Using the Quadratic Formula

Variable t cannot be equal to any of the values -2,0 since division by zero is not defined. Multiply both sides of the equation by t\left(t+2\right), the least common multiple of t,t+2.

$$\left(t+2\right)\times 4-t\left(4-\frac{1}{2}t\right)=0$$

Use the distributive property to multiply t+2 by 4.

$$4t+8-t\left(4-\frac{1}{2}t\right)=0$$

Use the distributive property to multiply t by 4-\frac{1}{2}t.

$$4t+8-\left(4t-\frac{1}{2}t^{2}\right)=0$$

To find the opposite of 4t-\frac{1}{2}t^{2}, find the opposite of each term.

$$4t+8-4t+\frac{1}{2}t^{2}=0$$

Combine 4t and -4t to get 0.

$$8+\frac{1}{2}t^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$\frac{1}{2}t^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{2} for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$t=\frac{0±\sqrt{0^{2}-4\times \frac{1}{2}\times 8}}{2\times \frac{1}{2}}$$

Square 0.

$$t=\frac{0±\sqrt{-4\times \frac{1}{2}\times 8}}{2\times \frac{1}{2}}$$

Multiply -4 times \frac{1}{2}.

$$t=\frac{0±\sqrt{-2\times 8}}{2\times \frac{1}{2}}$$

Multiply -2 times 8.

$$t=\frac{0±\sqrt{-16}}{2\times \frac{1}{2}}$$

Take the square root of -16.

$$t=\frac{0±4i}{2\times \frac{1}{2}}$$

Multiply 2 times \frac{1}{2}.

$$t=\frac{0±4i}{1}$$

Now solve the equation t=\frac{0±4i}{1} when ± is plus.

$$t=4i$$

Now solve the equation t=\frac{0±4i}{1} when ± is minus.

$$t=-4i$$

The equation is now solved.

$$t=4i t=-4i$$